由泊松跳变和Rosenblatt过程驱动的无穷延迟中立型随机积分微分方程的最优控制

IF 3.6 2区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Fractal and Fractional Pub Date : 2023-10-26 DOI:10.3390/fractalfract7110783
Dimplekumar Chalishajar, Ramkumar Kasinathan, Ravikumar Kasinathan
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引用次数: 1

摘要

研究了Hilbert空间中包含具体衰落记忆相空间的由泊松跳和Rosenblat过程驱动的具有无限延迟的中立型随机积分微分方程的最优控制问题,其中定义了随机过程的无限延迟的超前相空间。首先,利用随机分析理论、逐次逼近理论和grimer解算子理论,引入了保证温和解存在唯一性的条件。其次,我们证明了指数稳定性,其中包括均方指数稳定性,特别是包括解及其映射的指数稳定性。在此基础上,讨论了一类具有无穷时滞的随机偏积分微分方程的最优系统对的存在性要求。然后,我们探讨了一些例子来说明主要结果的潜力,主要是在热方程、过滤系统、交通信号灯系统和人体的生物过程中。最后对所研究的系统进行了数值模拟。这项工作是理论与实例和数值模拟的独特结合。
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Optimal Control for Neutral Stochastic Integrodifferential Equations with Infinite Delay Driven by Poisson Jumps and Rosenblatt Process
In this paper, we investigate the optimal control problems for a class of neutral stochastic integrodifferential equations (NSIDEs) with infinite delay driven by Poisson jumps and the Rosenblat process in Hilbert space involving concrete-fading memory-phase space, in which we define the advanced phase space for infinite delay for the stochastic process. First, we introduce conditions that ensure the existence and uniqueness of mild solutions using stochastic analysis theory, successive approximation, and Grimmer’s resolvent operator theory. Next, we prove exponential stability, which includes mean square exponential stability, and this especially includes the exponential stability of solutions and their maps. Following that, we discuss the existence requirements of an optimal pair of systems governed by stochastic partial integrodifferential equations with infinite delay. Then, we explore examples that illustrate the potential of the main result, mainly in the heat equation, filter system, traffic signal light systems, and the biological processes in the human body. We conclude with a numerical simulation of the system studied. This work is a unique combination of the theory with practical examples and a numerical simulation.
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来源期刊
Fractal and Fractional
Fractal and Fractional MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
CiteScore
4.60
自引率
18.50%
发文量
632
审稿时长
11 weeks
期刊介绍: Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.
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